[seqfan] Re: Please help to check A074140.

[David Wilson]

Given the definition of A074140, I was surprised at the regularity of the
values mod 10, but that can be explained.

However, the current b-file appears to be cut off in the middle of a(146).

> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of L. Edson
> Jeffery
> Sent: Saturday, August 03, 2013 4:15 PM
> To: seqfan at list.seqfan.eu
> Subject: [seqfan] Re: Please help to check A074140.
> 
> Peter,
> 
> For as close to "context-free" as one might get, see "An Introduction to
the
> Theory of Numbers" by Hardy and Wright, where an intuitive description of
> the algorithm is given but not formalized (since ordering is usually taken
to be
> irrelevant). I have the fifth edition (1979) of the book, but the
algorithm
> (which appears on page 273) is probably described as far back as the first
> edition from 1938 and likely did not originate even there.
> 
> Why such fancy and confusing terminology is necessary for all of this is
> beyond me. However, it appears that "Abramowitz and Stegun" just trivially
> reverses the order of the parts (not the partitions) of "Hardy and Wright"
> if that makes sense.
> 
> Example partitions of 4:
> 
> Hardy and Wright:      {4}, {3,1}, {2,2}, {2,1,1}, {1,1,1,1}
> 
> Abramowitz and Stegun: {4}, {1,3}, {2,2}, {1,1,2}, {1,1,1,1}
> 
> The conjugates of "Hardy and Wright" just give rise to the list of
partitions
> (not the parts) taken in reverse order:
> 
> {1,1,1,1}, {2,1,1}, {2,2}, {3,1}, {4}
> 
> which can be realized from certain rectangular arrays of dots described
> beginning on the same page (273) in the above book.
> 
> Ed Jeffery
> 
> >I have a hard time to understand this. I would like to have a
> *context-free* definition of all this stuff, not a heap of terms pointing
to one
> another. The very position of the term 'reverse' in these descriptions
often
> makes several readings possible.
> 
> >It would be very helpful to see algorithms which describe the meaning
> >of
> all these terms in a precise, unique way.
> 
> >Peter
> 
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